Solving Optimal Electric Vehicle Charger Deployment Problem
Abstract
:1. Introduction
 Building a comprehensive mathematical framework accommodating the particular complexity,
 Demonstrating our numerical computational framework for solving the facility location problem (FLP) representing the optimal location;
 Laying out an extensive comparative study among the optimization solving techniques as an effort to find the most efficient solver;
 Applying the findings to two realworld case studies representing an average and high density of EVs.
2. Related Work
2.1. Problem Formulation Approaches
2.1.1. Facility Location Problem (FLP)
2.1.2. Distance Optimization
2.1.3. Weight Assignment Techniques
2.1.4. Machine Learning Techniques
2.2. Solving Techniques
3. Problem Formulation
3.1. Spatial Setup
3.2. Formulation to Capacitated FLP
 i and j are indexes for an EV charging facility and a demanding area (or, equivalently, a customer), respectively.
 ${v}_{ij}$ gives the variable cost to obtain the electricity supplied to serve customer j.
 ${d}_{j}$ gauges the demand from customer j.
 ${y}_{ij}$ quantifies the fraction of the demand made by customer j and fulfilled by facility i.
 ${x}_{i}$ indicates whether facility i opens or not.
 ${s}_{i}$ denotes the sunken cost (also known as “fixed” cost) of opening a charging facility i.
 ${\mathsf{E}}_{i,j}$ defines the equity achieved at customer j via service from facility i.
 ${\mathsf{C}}_{i}$ and ${\mathsf{C}}_{\mathrm{min}}$ indicate the capacity of facility i and the required minimum capacity of any facility, respectively, both in the unit of kWh.
3.3. Unique Challenges
 C1: Large search spaces for domain and other variables;
 C2: Inexistence of polynomialtime numerical solving. techniques
4. Solving Techniques Development
4.1. Unique Challenges and Proposed Approaches
4.2. Comparison among Solving Techniques
4.3. Alternative Techniques
5. Case Study 1: Region with Average EV Density
5.1. CaseSpecific Refinement of Solving Method
5.2. Results and Discussion
Algorithm 1 SA implemented in this work 

6. Case Study 2: Region with High EV Density
6.1. CaseSpecific Refinement of Solving Method
6.1.1. Data Collection and Preprocessing
6.1.2. Data Integration
6.1.3. Training Methods
 Data Preparation: The collected and merged dataset undergoes preprocessing to ensure its suitability for training, including handling missing values, data normalization, and feature engineering.
 Training Process: Each selected model is trained using the prepared dataset, which is divided into training and validation sets. Performance evaluation metrics such as accuracy, precision, recall, and F1 score are utilized to assess the model’s performance during training.
 Model Evaluation: After training, the models are evaluated using the validation set to assess their predictive capabilities. The evaluation metrics are used to compare the models’ performance and identify the model with the highest accuracy or other desired performance metrics.
 Model Selection: Based on the evaluation results, the model demonstrating the best performance is selected as the final machine learning model for the site selection task.
6.2. Results and Discussions
 Installation criteria differ between DC fast chargers and level2 chargers. Significant differences in consistency are observed when training separately based on each charging station type or when training with both types together. Consequently, it can be concluded that chargers have been installed at locations that meet their respective criteria for both DC fast chargers and level2 chargers.
 Nonuniform distribution of reference data does not significantly affect training results. There is no significant difference in consistency between training based on nonuniformly distributed chargers and training based on grid points uniformly distributed at regular intervals. Thus, it can be concluded that the nonuniform distribution of data does not impact the training results.
 Buffer size influences data consistency. Decreasing the buffer size results in increased consistency. The reason for the decrease in consistency at buffer sizes below 125 m is that the polygon data used for learning is 250 m × 250 m grid data, resulting in buffers that do not contain data from the 125 m radius buffer size. This problem can be solved by using smaller grid data than 250 m × 250 m grid data during data preprocessing. In conclusion, this result shows that larger buffer sizes increase data redundancy and affect consistency.
7. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Literature  Contribution 

FLP  Formulation into MINLP for various realworld problems 
Distance Optimization  Stochastic analyses for location selection 
Weight Assignment Techniques  Demand prediction by assigning weights to data 
Machine Learning Techniques  More efficient weight assignment via priority prediction 
Solving Techniques  Exact or heuristic approaches to solve NPhard problems 
This Paper  Comprehensive feasibility study encompassing the aforementioned numerical techniques 
Solver  ${\mathit{x}}_{1}$  ${\mathit{x}}_{2}$  ⋯  ${\mathit{x}}_{10}$  Objective Value  Number of Iterations 

Integer Linear Programming  $4.4409\times {10}^{16}$  $4.4409\times {10}^{16}$  ⋯  $4.4409\times {10}^{16}$  0  0 
Pattern Search  0  0  ⋯  0  0  204 
Genetic Algorithm  −0.062657  0.042974  ⋯  −0.041941  1.4801  3907 
Particle Swarm  $7.2517\times {10}^{7}$  $2.5503\times {10}^{8}$  ⋯  $1.7757\times {10}^{6}$  $7.3\times {10}^{10}$  4320 
Simulated Annealing  $6.4039\times {10}^{5}$  −1.99  ⋯  0.00018799  3.9798  3008 
Surrogate Optimization  0.99678  1.9937  ⋯  1.9832  8.9671  200 
Model Name  Decision Tree  Support Vector Machine  Random Forest 

Consistency  0.6583  0.4295  0.7580 
Precision  0.6712  0.1845  0.7580 
Recall  0.6583  0.4295  0.7580 
F1Score  0.6593  0.2581  0.7509 
Setting Condition  Buffer Size  Consistency  

Baseline  Public DC fast chargers and random point  1.13 km  0.7580 
a. Charging Station Type  Public level2 chargers and random point  1.13 km  0.7678 
Public DC fast chargers and public level2 chargers and random point  1.13 km  0.6284  
b. Uniform Distribution of Reference Data  Center point of grid data  1.13 km  0.7649 
c. Buffer size  Public DC fast chargers and random point  700 m  0.8176 
600 m  0.8355  
500 m  0.8611  
400 m  0.8743  
300 m  0.9003  
200 m  0.9182  
150 m  0.9348  
125 m  0.9395  
100 m  0.9293  
50 m  0.8969 
Data  Variable Importance [%] 

POI  16.9264 
Surface  12.9745 
Building0  11.3435 
Work_Population  9.4463 
Building3  8.1137 
Traffic  7.3983 
Building1  6.768 
Flow_Population  5.7931 
Car  5.4492 
EV_Car  5.3769 
Parking  4.2025 
Tour  3.563 
Building2  2.6447 
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Kim, S.; Jeong, Y.; Nam, J.W. Solving Optimal Electric Vehicle Charger Deployment Problem. Appl. Sci. 2024, 14, 5092. https://doi.org/10.3390/app14125092
Kim S, Jeong Y, Nam JW. Solving Optimal Electric Vehicle Charger Deployment Problem. Applied Sciences. 2024; 14(12):5092. https://doi.org/10.3390/app14125092
Chicago/Turabian StyleKim, Seungmo, Yeonho Jeong, and JaeWon Nam. 2024. "Solving Optimal Electric Vehicle Charger Deployment Problem" Applied Sciences 14, no. 12: 5092. https://doi.org/10.3390/app14125092